Answer:
see the explanation
Step-by-step explanation:
we have
![x^2+6x+y^2-16y=-9](https://tex.z-dn.net/?f=x%5E2%2B6x%2By%5E2-16y%3D-9)
<u><em>Convert the equation of the circle in center radius form</em></u>
Group terms that contain the same variable
![(x^2+6x)+(y^2-16y)=-9](https://tex.z-dn.net/?f=%28x%5E2%2B6x%29%2B%28y%5E2-16y%29%3D-9)
Complete the square twice. Remember to balance the equation by adding the same constants to each side
![(x^2+6x+9)+(y^2-16y+64)=-9+9+64](https://tex.z-dn.net/?f=%28x%5E2%2B6x%2B9%29%2B%28y%5E2-16y%2B64%29%3D-9%2B9%2B64)
![(x^2+6x+9)+(y^2-16y+64)=64](https://tex.z-dn.net/?f=%28x%5E2%2B6x%2B9%29%2B%28y%5E2-16y%2B64%29%3D64)
Rewrite as perfect squares
![(x+3)^2+(y-8)^2=8^2](https://tex.z-dn.net/?f=%28x%2B3%29%5E2%2B%28y-8%29%5E2%3D8%5E2)
The center of the circle is (-3,8)
The radius of the circle is 8 units
<u><em>Verify each statement</em></u>
A. The center of the circle is (3,-8).
False
The center of the circle is (-3,8)
B. The circle is tangent to the x-axis
True
The circle is tangent to x=5 and x=-11 and is tangent to y=0 and y=16
Remember that y=0 is the x-axis
C. The circle has a radius of 64
False
The radius of the circle is 8 units